Systematic bias in studies of consumer functional responses

Does mutual interference stabilize prey-predator model with Bazykin-Crowley-Martin trophic function?

We investigated a system of ordinary differential equations that describes the dynamics of prey and predator populations, taking into account the Allee effect affecting the reproduction of the predator population, and mutual interference amongst predators, which is modeled with the Bazykin-Crowley-Martin (BCM) trophic function. Bifurcation analysis revealed a rich spectrum of bifurcations occurring in the system. In particular, analytical conditions for the saddle-node, Hopf, cusp, and Bogdanov-Takens bifurcations were derived for the model parameters, quantifying the strength of the predator interference, the Allee effect, and the predation efficiency. Numerical simulations verify and illustrate the analytical findings. The main purpose of the study was to test whether the mutual interference in the model with BCM trophic function provides a stabilizing or destabilizing effect on the system dynamics. The obtained results suggest that the model demonstrates qualitatively the same pattern concerning varying the interference strength as other predator-dependent models: both low and very high interference levels increase the risk of predator extinction, while moderate interference has a favorable effect on the stability and resilience of the prey-predator system.

Trophic tug-of-war: Coexistence mechanisms within and across trophic levels

Ecological communities encompass rich diversity across multiple trophic levels. While modern coexistence theory has been widely applied to understand community assembly, its traditional formalism only allows assembly within a single trophic level. Here, using an expanded definition of niche and fitness differences applicable to multitrophic communities, we study how diversity within and across trophic levels affects species coexistence. If each trophic level is analysed separately, both lower- and higher trophic levels are governed by the same coexistence mechanisms. In contrast, if the multitrophic community is analysed as a whole, different trophic levels are governed by different coexistence mechanisms: coexistence at lower trophic levels is predominantly limited by fitness differences, whereas coexistence at higher trophic levels is predominantly limited by niche differences. This dichotomy in coexistence mechanisms is supported by theoretical derivations, simulations of phenomenological and trait-based models, and a case study of a primeval forest ecosystem. Our work provides a general and testable prediction of coexistence mechanism operating in multitrophic communities.

Predator-mediated interactions through changes in predator home range size can lead to local prey exclusion

The strength of indirect biotic interactions is difficult to quantify in the wild and can alter community composition. To investigate whether the presence of a prey species affects the population growth rate of another prey species, we quantified predator-mediated interaction strength using a multi-prey mechanistic model of predation and a population matrix model. Models were parametrized using behavioural, demographic and experimental data from a vertebrate community that includes the arctic fox (Vulpes lagopus), a predator feeding on lemmings and eggs of various species such as sandpipers and geese. We show that the positive effects of the goose colony on sandpiper nesting success (due to reduction of search time for sandpiper nests) were outweighed by the negative effect of an increase in fox density. The fox numerical response was driven by changes in home range size. As a result, the net interaction from the presence of geese was negative and could lead to local exclusion of sandpipers. Our study provides a rare empirically based model that integrates mechanistic multi-species functional responses and behavioural processes underlying the predator numerical response. This is an important step forward in our ability to quantify the consequences of predation for community structure and dynamics.

Adaptive experimental design produces superior and more efficient estimates of predator functional response

Ecological dynamics are strongly influenced by the relationship between prey density and predator feeding behavior-that is, the predatory functional response. A useful understanding of this relationship requires us to distinguish between competing models of the functional response, and to robustly estimate the model parameters. Recent advances in this topic have revealed bias in model comparison, as well as in model parameter estimation in functional response studies, mainly attributed to the quality of data. Here, we propose that an adaptive experimental design framework can mitigate these challenges. We then present the first practical demonstration of the improvements it offers over standard experimental design. Our results reveal that adaptive design can efficiently identify the preferred functional response model among the competing models, and can produce much more precise posterior distributions for the estimated functional response parameters. By increasing the efficiency of experimentation, adaptive experimental design will lead to reduced logistical burden.

Origins of life: first came evolutionary dynamics

When life arose from prebiotic molecules 3.5 billion years ago, what came first? Informational molecules (RNA, DNA), functional ones (proteins), or something else? We argue here for a different logic: rather than seeking a molecule type, we seek a dynamical process. Biology required an ability to evolve before it could choose and optimise materials. We hypothesise that the evolution process was rooted in the peptide folding process. Modelling shows how short random peptides can collapse in water and catalyse the elongation of others, powering both increased folding stability and emergent autocatalysis through a disorder-to-order process.

Empirical evidence of type III functional responses and why it remains rare

More than 70 years after its introduction, the framework of resource density-dependent consumption rates, also known as predator-prey functional responses, remains a core concept in population and food web ecology. Initially, three types of responses were defined: linear (type I), hyperbolic (type II), and sigmoid (type III). Due to its potential to stabilize consumer-resource population dynamics, the sigmoid type III functional response immediately became a “holy grail” in population ecology. However, experimentally proving that type III functional responses exist, whether in controlled laboratory systems or in nature, was challenging. While theoretical and practical advances make identifying type III responses easier today, decades of research have brought only a limited number of studies that provide empirical evidence for type III response curves. Here, we review this evidence from laboratory- and field-based studies published during the last two decades. We found 107 studies that reported type III responses, but these studies ranged across various taxa, interaction types, and ecosystems. To put these studies into context, we also discuss the various biological mechanisms that may lead to the emergence of type III responses. We summarize how three different and mutually independent intricacies bedevil the empirical documentation of type III responses: (1) challenges in statistical modeling of functional responses, (2) inadequate resource density ranges and spacing, and (3) biologically meaningful and realistic design of experimental arenas. Finally, we provide guidelines on how the field should move forward based on these considerations.

Predator feeding rates may often be unsaturated under typical prey densities

Predator feeding rates (described by their functional response) must saturate at high prey densities. Although thousands of manipulative functional response experiments show feeding rate saturation at high densities under controlled conditions, it remains unclear how saturated feeding rates are at natural prey densities. The general degree of feeding rate saturation has important implications for the processes determining feeding rates and how they respond to changes in prey density. To address this, we linked two databases-one of functional response parameters and one on mass-abundance scaling-through prey mass to calculate a feeding rate saturation index. We find that: (1) feeding rates may commonly be unsaturated and (2) the degree of saturation varies with predator and prey taxonomic identities and body sizes, habitat, interaction dimension and temperature. These results reshape our conceptualisation of predator-prey interactions in nature and suggest new research on the ecological and evolutionary implications of unsaturated feeding rates.

Food web functional responses

This article reviews the nature of functional responses that have commonly been used to represent feeding relationships in the ecological literature. It compares these with the range of functional response forms that are likely to characterize species in natural communities. The latter set of responses involves many more variables. The article reviews the history of functional response models, and examines previous work that has allowed the functional response of a predator to a single type of prey to depend on additional variables beyond the abundance of that prey type. While a number of more complex functional responses have been discussed over the years, many variables affecting feeding rates are still typically omitted from models of food webs. The influences on functional responses from trophic levels above that of the predator or below that of the prey are particularly likely to be ignored, although models and data have suggested that they can have large effects on the functional response. The influences of adaptive behavior and of the time-scale of response measurement are also too often ignored. Some of the known and unknown consequences of these omissions are discussed.

Functional Responses Shape Node and Network Level Properties of a Simplified Boreal Food Web

Ecological communities are fundamentally connected through a network of trophic interactions that are often complex and difficult to model. Substantial variation exists in the nature and magnitude of these interactions across various predators and prey and through time. However, the empirical data needed to characterize these relationships are difficult to obtain in natural systems, even for relatively simple food webs. Consequently, prey-dependent relationships and specifically the hyperbolic form (Holling’s Type II), in which prey consumption increases with prey density but ultimately becomes saturated or limited by the time spent handling prey, are most widely used albeit often without knowledge of their appropriateness. Here, we investigate the sensitivity of a simplified food web model for a natural, boreal system in the Kluane region of the Yukon, Canada to the type of functional response used. Intensive study of this community has permitted best-fit functional response relationships to be determined, which comprise linear (type I), hyperbolic (type II), sigmoidal (type III), prey- and ratio-dependent relationships, and inverse relationships where kill rates of alternate prey are driven by densities of the focal prey. We compare node- and network-level properties for a food web where interaction strengths are estimated using best-fit functional responses to one where interaction strengths are estimated exclusively using prey-dependent hyperbolic functional responses. We show that hyperbolic functional responses alone fail to capture important ecological interactions such as prey switching, surplus killing and caching, and predator interference, that in turn affect estimates of cumulative kill rates, vulnerability of prey, generality of predators, and connectance. Exclusive use of hyperbolic functional responses also affected trends observed in these metrics over time and underestimated annual variation in several metrics, which is important given that interaction strengths are typically estimated over relatively short time periods. Our findings highlight the need for more comprehensive research aimed at characterizing functional response relationships when modeling predator-prey interactions and food web structure and function, as we work toward a mechanistic understanding linking food web structure and community dynamics in natural systems.

Quantifying predator functional responses under field conditions reveals interactive effects of temperature and interference with sex and stage

Predator functional responses describe predator feeding rates and are central to predator–prey theory. Originally defined as the relationship between predator feeding rates and prey densities, it is now well known that functional responses are shaped by a multitude of factors. However, much of our knowledge about how these factors influence functional responses is based on laboratory studies that are generally logistically constrained to examining only a few factors simultaneously and that have unclear links to the conditions organisms experience in the field.

We apply an observational approach for measuring functional responses to understand how sex/stage differences, temperature and predator densities interact to influence the functional response of zebra jumping spiders on midges under natural conditions.

We used field surveys of jumping spiders to infer their feeding rates and examine the relationships between feeding rates, sex/stage, midge density, predator density and temperature using generalized additive models. We then used the relationships supported by the models to fit parametric functional responses to the data.

We find that feeding rates of zebra jumping spiders follow some expectations from previous laboratory studies such as increasing feeding rates with body size and decreasing feeding rates with predator densities. However, in contrast to previous results, our results also show a lack of temperature response in spider feeding rates and differential decreases in the feeding rates of females and juveniles with densities of different spider sexes/stages.

Our results illustrate the multidimensional nature of functional responses in natural settings and reveal how factors influencing functional responses can interact with one another through behaviour and morphology. Further studies investigating the influence of multiple mechanisms on predator functional responses under field conditions will increase our understanding of the drivers of predator–prey interaction strengths and their consequences for communities and ecosystems.

The Issue Isn’t Which Model of Consumer Interference Is Right, but Which One Is Least Wrong

Empirical observations and an analogy with the history of ballistics illuminate the ongoing debate about the default choice for types of functional responses, based on consumer interference. The two ideal views of consumer interference are: (1) There is no direct mutual interference among consumers (“prey-dependence”), and (2) Consumers show strong mutual interference, the functional response depending on the number of prey per consumer (“ratio-dependence”). Each of these minimal-information concepts are what we refer to as “root” models, of limited accuracy in themselves, but they are the base upon which we erect complex models for specific, real-world cases. We argue that the ratio dependent view coincides more naturally with the way we model the dynamics of any population, and taken alone it is the model more consistent with empirical observations. Both root models often will give the “wrong answer” when applied directly to real world cases. Nevertheless, one root model may be “less wrong” than the other. This is not unlike developments 400 years ago in physics, when two root models competed in ballistics. Galileo’s demonstration that the default trajectory of a projectile is a parabola eventually replaced what had been the dominant root model since Aristotle. Both ballistic root models are inaccurate in the presence of air friction, but the parabolic model is, overall, less wrong. We argue that the ratio-dependent model, like the parabolic trajectory, is the “less wrong” and it is therefore a natural view from which to start thinking about consumer-resource interaction and developing more elaborate models.

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

The functional response (trophic function or individual ration) quantifies the average amount of prey consumed per unit of time by a single predator. Since the seminal Lotka-Volterra model, it is a key element of the predation theory. Holling has enhanced the theory by classifying prey-dependent functional responses into three types that long remained a generally accepted basis of modeling predator-prey interactions. However, contradictions between the observed dynamics of natural ecosystems and the properties of predator-prey models with Holling-type trophic functions, such as the paradox of enrichment, the paradox of biological control, and the paradoxical enrichment response mediated by trophic cascades, required further improvement of the theory. This led to the idea of the inclusion of predator interference into the trophic function. Various functional responses depending on both prey and predator densities have been suggested and compared in their performance to fit observed data. At the end of the 1980s, Arditi and Ginzburg stimulated a lively debate having a strong impact on predation theory. They proposed the concept of a spectrum of predator-dependent trophic functions, with two opposite edges being the prey-dependent and the ratio-dependent cases, and they suggested revising the theory by using the ratio-dependent edge of the spectrum as a null model of predator interference. Ratio-dependence offers the simplest way of accounting for mutual interference in predator-prey models, resolving the abovementioned contradictions between theory and natural observations. Depending on the practical needs and the availability of observations, the more detailed models can be built on this theoretical basis.

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

The Stochastic Nature of Functional Responses

Functional responses are non-linear functions commonly used to describe the variation in the rate of consumption of resources by a consumer. They have been widely used in both theoretical and empirical studies, but a comprehensive understanding of their parameters at different levels of description remains elusive. Here, by depicting consumers and resources as stochastic systems of interacting particles, we present a minimal set of reactions for consumer resource dynamics. We rigorously derived the corresponding system of ODEs, from which we obtained via asymptotic expansions classical 2D consumer-resource dynamics, characterized by different functional responses. We also derived functional responses by focusing on the subset of reactions describing only the feeding process. This involves fixing the total number of consumers and resources, which we call chemostatic conditions. By comparing these two ways of deriving functional responses, we showed that classical functional response parameters in effective 2D consumer-resource dynamics differ from the same parameters obtained by measuring (or deriving) functional responses for typical feeding experiments under chemostatic conditions, which points to potential errors in interpreting empirical data. We finally discuss possible generalizations of our models to systems with multiple consumers and more complex population structures, including spatial dynamics. Our stochastic approach builds on fundamental ecological processes and has natural connections to basic ecological theory.

Increasing availability of palatable prey induces predator-dependence and increases predation on unpalatable prey

Understanding the factors governing predation remains a top priority in ecology. Using a dragonfly nymph-tadpole system, we experimentally varied predator density, prey density, and prey species ratio to investigate: (i) whether predator interference varies between prey types that differ in palatability, (ii) whether adding alternate prey influences the magnitude of predator interference, and (iii) whether patterns of prey selection vary according to the predictions of optimal diet theory. In single-prey foraging trials, predation of palatable leopard frog tadpoles was limited by prey availability and predator interference, whereas predation of unpalatable toad tadpoles was limited by handling time. Adding unpalatable prey did not affect the predator’s kill rate of palatable prey, but the presence of palatable prey increased the influence of predator density on the kill rate of unpalatable prey and reduced unpalatable prey handling time. Prey selection did not change with shifts in the relative abundance of prey types. Instead, predators selected easy-to-capture unpalatable prey at low total densities and harder-to-capture palatable prey at high densities. These results improve our understanding of generalist predation in communities with mobile prey, and illustrate that characteristics of the prey types involved govern the extent to which alternate prey influence the predator’s kill rate.

Hidden layers of density dependence in consumer feeding rates

Functional responses relate a consumer's feeding rates to variation in its abiotic and biotic environment, providing insight into consumer behaviour and fitness, and underpinning population and food-web dynamics. Despite their broad relevance and long-standing history, we show here that the types of density dependence found in classic resource- and consumer-dependent functional-response models equate to strong and often untenable assumptions about the independence of processes underlying feeding rates. We first demonstrate mathematically how to quantify non-independence between feeding and consumer interference and between feeding on multiple resources. We then analyse two large collections of functional-response data sets to show that non-independence is pervasive and borne out in previously hidden forms of density dependence. Our results provide a new lens through which to view variation in consumer feeding rates and disentangle the biological underpinnings of species interactions in multi-species contexts.